A smartly dressed woman hammers away at an old-style typewriter in a drawing room. She is the real-life American journalist and conspiracy theorist Dorothy Kilgallen (Janie Dee) and bears the gimlet-eyed look of Angela Lansbury in Murder, She Wrote.

Torben Betts’s play could be called Marilyn, She Wrote. It is the 1960s, Marilyn Monroe has been found dead in her bed and Kilgallen thinks both John F Kennedy and his brother Robert F Kennedy (Jolyon Coy) had something to do with it. Her investigations form part of an unpublished book which suggests links between a political cover-up and underworld crime that, she argues, led to Monroe’s death aged 36.

Kilgallen receives a threatening phone call from a stalker just as the babysitter, Flo (Gloria Obianyo), arrives.…